Digital Phase Correction for Dual-Comb Spectroscopy*

Dual-comb spectroscopy (DCS) maps optical spectra to a radio-frequency (RF) comb by interfering two mode-locked lasers with slightly different repetition rates. Comb-tooth-resolved detection requires precise control of both the repetition rate (f_rep)​ and the carrier–envelope-offset (CEO) frequency (f_ceo​) for both lasers, as fluctuations in f_rep​ and f_ceo degrade comb coherence and limit coherent averaging.  While f_rep can be easily measured and stabilized, f_ceo typically requires an f-2f interferometer.

We demonstrate a continuous-wave (CW) laser-assisted scheme that replaces f–2f CEO stabilization with digital phase correction. A narrow-linewidth CW laser is beaten with each comb to generate references that track the instantaneous CEO frequency, which are processed by a software algorithm to remove relative f_ceo drift and timing jitter. This approach enables comb-tooth-resolved spectra from free-running combs and is validated by resolving both linear absorption and nonlinear dipole–dipole interactions in rubidium vapor.